Using a mixer (I use a stand mixer), put the peanut butter, extract, sugar and salt in a bowl and slowly cream together (I used the scraper paddle attachment) until smooth. Then, add 1 cup of the half-and-half (and I switched to the whisk attachment) and beat on low speed until well mixed. Lastly add the rest of the half-and-half and heavy cream and whisk at medium speed (just slower than "splatter everywhere" speed) for 3-5 minutes, until the liquid starts to thicken a little.

Pour the mixture into whatever ice cream maker you use and process for 25-30 minutes (or whatever the manufacturer's directions are).

It will be soft but edible when done. Let it sit in the freezer overnight to harden up.